1/22/2020 10:01:01 AM | MATH 27 Course Outline as of Summer 2019
| Changed Course |

CATALOG INFORMATION |
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Discipline and Nbr: MATH 27 | Title: PRECALC ALG AND TRIG | |

Full Title: Precalculus Algebra and Trigonometry | ||

Last Reviewed:10/22/2018 |

Units | Course Hours per Week | Nbr of Weeks | Course Hours Total | ||||
---|---|---|---|---|---|---|---|

Maximum | 5.00 | Lecture Scheduled | 5.00 | 17.5 max. | Lecture Scheduled | 87.50 | |

Minimum | 5.00 | Lab Scheduled | 0 | 8 min. | Lab Scheduled | 0 | |

Contact DHR | 0 | Contact DHR | 0 | ||||

Contact Total | 5.00 | Contact Total | 87.50 | ||||

Non-contact DHR | 0 | Non-contact DHR Total | 0 |

Total Out of Class Hours: 175.00 | Total Student Learning Hours: 262.50 |

Grading: Grade Only

Repeatability: 00 - Two Repeats if Grade was D, F, NC, or NP

Also Listed As:

Formerly: MATH 57

**Catalog Description:**

College algebra and trigonometry topics, including equations, expressions, functions, inverse functions, and graphs. Also includes polar coordinates, parametric equations, complex numbers, vectors, sequences and series.

**Prerequisites/Corequisites:**

Completion of MATH 156 OR MATH 154 OR MATH 155 or appropriate placement based on AB 705 mandates

**Recommended Preparation:**

**Limits on Enrollment:**

**Schedule of Classes Information**

Description:

College algebra and trigonometry topics, including equations, expressions, functions, inverse functions, and graphs. Also includes polar coordinates, parametric equations, complex numbers, vectors, sequences and series.

(Grade Only)

Prerequisites:Completion of MATH 156 OR MATH 154 OR MATH 155 or appropriate placement based on AB 705 mandates

Recommended:

Limits on Enrollment:

Transfer Credit:CSU;UC.

Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

__ARTICULATION, MAJOR, and CERTIFICATION INFORMATION__Associate Degree: | Effective: | Fall 1981 | Inactive: | ||

Area: | B MC | Communication and Analytical Thinking Math Competency |
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CSU GE: | Transfer Area | Effective: | Inactive: | ||

B4 | Math/Quantitative Reasoning | Fall 1996 | |||

B4 | Math/Quantitative Reasoning | Fall 1981 | Spring 1984 | ||

IGETC: | Transfer Area | Effective: | Inactive: | ||

2A | Mathematical Concepts & Quantitative Reasoning | Fall 1998 | |||

CSU Transfer: | Transferable | Effective: | Fall 1981 | Inactive: | |

UC Transfer: | Transferable | Effective: | Fall 1998 | Inactive: | |

C-ID: |

Certificate/Major Applicable: Major Applicable Course

__COURSE CONTENT__**Student Learning Outcomes:**

Upon completion of the course, students will be able to:

1. Perform advanced operations with functions (polynomial, rational, absolute value, radical,

exponential, and logarithmic), understand the characteristics and graphs of these

functions, and apply knowledge to modeling problems.

2. Solve selected algebraic equations symbolically over the complex numbers, and solve

polynomial, rational, absolute value, radical, exponential, and logarithmic equations

graphically and symbolically over the real numbers.

3. Define and graph the six trigonometric functions and their inverses, solve equations involving

trigonometric functions symbolically and graphically, and verify trigonometric identities.

4. Use trigonometric functions, identities, and Laws of Sines and Cosines to solve applications

problems.

5. Define, graph, and demonstrate appropriate applications of vectors, complex numbers, polar

coordinates, parametric equations, and inverse functions.

**Objectives:**

During this course, students will:

1. Perform advanced operations with functions (using symbolic, graphical, and numerical

representations) and apply knowledge to application and modeling problems.

2. Define and graph inverse functions.

3. Define and apply the trigonometric functions, using right triangle and unit circle approaches,

and using degree and radian measures.

4. Identify and interpret characteristics of functions (including intercepts, turning points, extreme

values, intervals of positive/negative/increasing/decreasing value, transformations,

symmetry, asymptotes, and holes).

5. Graph polynomial, rational, absolute value, radical, exponential, logarithmic, trigonometric,

and inverse trigonometric functions.

6. Verify and apply trigonometric identities.

7. Solve equations symbolically and graphically (involving polynomial, rational, absolute value,

radical, exponential, logarithmic, and trigonometric functions) over the real numbers; and,

as appropriate, the complex numbers.

8. Solve application and modeling problems using the trigonometric functions, identities, and the

Laws of Sines and Cosines.

9. Represent complex numbers in trigonometric form and perform operations.

10. Graph piecewise-defined functions and parametric equations.

11. Use vectors to model applications in mathematics and science.

**Topics and Scope**

I. Equations and Inequalities

A. Graphical and algebraic solutions to radical and quadratic form equations

B. Graphical and algebraic solutions to absolute value equations and inequalities

II. Analysis of Functions and Their Graphs

A. Definition

B. Notation

C. Domain

D. Range

E. Operations, including difference quotients and composition of functions

F. Catalog of functions

G. Symmetry (even and odd functions)

H. Transformations of graphs (shifts, scaling, reflections)

I. Modeling

III. Polynomial and Rational Functions

A. Linear, quadratic, and polynomial functions of higher degree, and their graphs

B. Long division of polynomials

C. Graphs of rational functions

D. Asymptotes and holes

E. Introduction to limit concepts and notation

F. Solutions of polynomial and rational equations and inequalities, using real numbers and

complex numbers as appropriate

IV. Inverse, Exponential, and Logarithmic Functions

A. Definitions

B. Properties

C. Graphs

D. Equations

E. Applications

V. Trigonometric Functions

A. Radian and degree measures of angles

1. Arc length

2. Area of a sector

3. Linear and angular velocity

B. Right triangle and unit circle definitions

C. Characteristics of trigonometric functions

VI. Identities and Conditional Equations

A. Fundamental identities

B. Sum and difference identities

C. Related identities and their derivations

D. Conditional trigonometric equations and applications

VII. Graphical Representation of Trigonometric Functions

A. Amplitude

B. Reflections

C. Period

D. Phase (horizontal) shift

E. Vertical shifts

VIII. Inverse Trigonometric Functions

A. Definitions

B. Properties

C. Graphs

IX. Solutions of Triangles

A. Right triangles

B. Oblique triangles

C. Laws of Sines and Cosines

D. Applications

X. Complex Numbers, Polar Coordinates, and Parametric Equations

A. Definitions

B. Operations

C. Graphical representation of complex numbers

D. DeMoivre's Theorem

E. Polar coordinates

F. Parametric equations

XI. Two Dimensional Vectors

A. Geometric and analytic definitions

B. Algebra of vectors

C. Trigonometric form of vectors

D. Dot product

E. Applications

XII. Sequences and Series

A. Introduction to finite and infinite sequence and series (sigma) notation

B. Finite and infinite geometric sequences and series

C. Summation of powers of integers

D. Binomial Expansion

1. Factorial notation

2. Pascal's Triangle and/or binomial coefficients

**Assignments:**

1. Reading outside of class (0-60 pages per week)

2. Problem sets (1-8 per week)

3. Quizzes (0-4 per week)

4. Projects (0-10)

5. Exams (3-8)

6. Final exam

**Methods of Evaluation/Basis of Grade.**

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing. | Writing 0 - 0% |
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None | |||

This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course. | |||

Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills. | Problem Solving 5 - 20% |
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Problems sets | |||

Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations 0 - 0% |
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None | |||

Exams: All forms of formal testing, other than skill performance exams. | Exams 70 - 95% |
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Exams and quizzes | |||

Other: Includes any assessment tools that do not logically fit into the above categories. | Other Category 0 - 10% |
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Projects |

**Representative Textbooks and Materials:**

Precalculus: Enhanced with Graphing Utilities. 7th ed. Sullivan, Michael and Sullivan III, Michael. Pearson. 2016

Precalculus. 3rd corrected ed. Stitz, Carl and Zeager, Jeffrey. Open Source Text. 2013 (classic)